Question

One side of a right triangle has a length of 12 feet. Which of the following could be lengths for the two other sides of the right triangle?

I. 5 feet and 13 feet
II. 9 feet and V63 feet
III. V2 feet and V10 feet
A. I,II, and I
B. I and II only
C. I only
D. I and III only​

Answer 1

The lengths that could be the other two sides of the right triangle are 5 feet and 13 feet, and 9 feet and the square root of 63 feet.

Step-by-step explanation:

A right triangle has one side with a length of 12 feet. In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Using this theorem, we can determine whether the given lengths can form a right triangle:

I. 5 feet and 13 feet:
169
We can see that 169 is equal to 13², so this length combination could form a right triangle.

II. 9 feet and √63 feet:
225
We can see that 225 is equal to 15², so this length combination could form a right triangle.

III. √2 feet and √10 feet:
144 + 2 = 146
This combination does not satisfy the Pythagorean theorem, so it could not form a right triangle.

Therefore, the lengths that could be the other two sides of the right triangle are I. 5 feet and 13 feet, and II. 9 feet and √63 feet.